Positioning apparatus and method for manufacturing same

ABSTRACT

A positioning apparatus includes a wafer chuck which retains a wafer and a hollow plate unit which retains the chuck, which is composed of a ceramic material in an integral, hollow structure having a hollow section, the hollow section having a rib structure which serves to increase the natural frequency of the hollow plate unit with respect to torsional mode vibration, and which has holes for providing connection between the interior and exterior of the hollow section. The rib structure is constructed such that a rib unit having a rectangular shape in cross section, the sides thereof extending along X and Y fine movement directions, and a rig unit having a diamond shape in cross section are alternately disposed inside each other and are bonded to each other.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a positioning apparatus for a stage orthe like used in an apparatus or method for manufacturing devices suchas semiconductor devices and liquid crystal displays. The positioningapparatus is used in, for example, a projection exposure apparatus,various precise processing apparatuses and measuring apparatuses, etc.,for moving and positioning a substrate such as a semiconductor wafer, amask, and a reticle at high speed and with high accuracy. In addition,the present invention may also be applied to a method for manufacturinga semiconductor device by using an exposure apparatus incorporating sucha positioning device.

2. Description of the Related Art

FIG. 12 shows a perspective view of an XY stage as an example of a knownpositioning device. A positioning device of this type is disclosed in,for example, Japanese Unexamined Patent Application Publication No.8-229759.

In FIG. 12, reference numeral 42 denotes a base which supports a stagedevice and includes a reference surface 43, and reference numeral 38denotes a fixed Y guide which is fixed to the base 42 and whose sidesurface serves as a reference surface. In addition, reference numeral 37denotes a Y stage which serves as a moving body. The Y stage 37 isguided by the fixed Y guide 38 and is moved in a Y direction by Y linearmotors 41 disposed at both ends thereof, each Y linear motor 41including a fixed member 39 and a movable member 40. Reference numeral32 denotes an X stage which includes movable members (not shown) of Xlinear motors. The X stage 32 is guided by an X guide 33 provided on theY stage 37 and receives a thrust from fixed members 34 of the X linearmotors which are also provided on the Y stage 37.

As shown in FIG. 12, a top plate 31 of the X stage 32 has a flat shape,and an X-direction mirror 45 and a Y-direction mirror 46 used forposition measurement in the X and Y directions, respectively, aredisposed on the top plate 31. The position measurement is performed byirradiating the mirrors with a laser beam and detecting the reflectedlight.

When a θZT driving mechanism shown in FIG. 16 is installed in this stagedevice, movements in a Z direction, which is a direction parallel to,for example, an optical axis of an exposure system, and in rotationaldirections around the X, Y, and Z axes (θ_(x), θ_(y), θ_(z)) are alsopossible.

The upper portion of the X stage 32 shown in FIG. 12 corresponds to abase plate 151 shown in FIG. 16. A cylindrical fixed member 202 isprovided on the base plate 151, and a porous pad 207 attached to thefixed member 202 retains an internal surface of a guiding member 203without contacting it. The guiding member 203 is formed integrally witha top plate 204, which corresponds to the top plate 31 used forsupporting a wafer and a wafer chuck (not shown). The base plate 151 canbe rotated around the central axis thereof by a θ linear motor 216, andcan be reciprocated in the vertical direction in FIG. 16 by Z linearmotors 215 which are arranged along the circumferential direction atconstant intervals.

FIG. 13 is a block diagram for each degree of freedom in the knownpositioning apparatus. Reference numeral 57 denotes mechanicalcharacteristics Go of the positioning apparatus. According to themechanical characteristics Go, a displacement x is output when a force fis input. Reference numeral 58 denotes controller characteristics Gcincluding characteristics of a proportional-integral-differential (PID)controller, amplifier characteristics, and stabilization filters.According to the controller characteristics Gc, a predetermined force fis output when the difference obtained by subtracting the displacement xfrom a desired position xr is input. For example, in position control inthe X and Y directions, the output of a laser interferometer is used todetermine the displacement x. The performance of the positioningapparatus is determined by how quickly and accurately the desiredposition can be tracked in each degree of freedom.

FIG. 14 is a diagram showing gain/phase characteristics of the controlsystem of the known positioning apparatus. The gain/phasecharacteristics shown in FIG. 14 are the combination of the mechanicalcharacteristics Go and the controller characteristics Gc shown in FIG.13, and are called loop transfer characteristics. In order to obtainhigh-speed, high-accuracy tracking performance, the gain characteristicsof the positioning apparatus are preferably made as high as possible.However, the mechanical characteristics Go include various naturalfrequencies, and the plate-shaped stage component 31 used in the knownpositioning apparatus may have a natural frequency with a high peak(weak damping) in a low-frequency region (from 300 Hz).

When vibration of the stage components occurs, the mirrors mounted onthe stage for position measurement also vibrate and the positioningaccuracy is reduced.

In addition, since oscillation occurs at the natural frequency when thegain is too high, the gain characteristics of the control system arelimited. In FIG. 14, the zero-crossing frequency, which serves as anindex of the gain level, is approximately 40 Hz.

Accordingly, it is necessary to suppress the peak by using stabilizationfilters such as low-pass filters and notch filters. Alternatively, thesystem is designed such that the natural frequency is increased to ahigh-frequency region.

In Japanese Unexamined Patent Application Publication No. 11-142555, forexample, a stage component having a hollow structure is disclosed. Withreference to FIG. 15, reference numeral 411 denotes a top plate unitincluded in an X stage. The top plate unit 411 is formed of ceramic andhas a hollow structure as shown in the figure. This hollow structure 421is constructed of two or more ceramic members and has an injection hole431 at the bottom thereof. After the two or more members are baked, theyare bonded together by a resintering process. In the resinteringprocess, the members are generally bonded together by glass bondingusing an alumina-based material having a coefficient of thermalexpansion which is close to that of the members. However, when amaterial having a small coefficient of thermal expansion is used inorder to suppress the thermal deformation of the top plate unit 411,there is the risk that sufficient bonding strength cannot be obtained.In addition, when an adhesive is used for bonding the members together,there is the risk that sufficient adhesive strength and adhesivereliability cannot be obtained.

In the above-described example, in order to move the top platesupporting the substrate, such as a wafer, to a predetermined positionin the XY plane, the base plate is moved in the X and Y directions bythe XY stage unit while the position of the top plate in the XY plane isdetermined by laser interferometers. In addition, the top plate receivesa driving force from the base plate through radial air bearings. The topplate thus moves to the predetermined position. At this time, the topplate and the base plate preferably move together. However, inactuality, the driving force is applied to the top plate with a phaselag with respect to the movement of the base plate in correspondencewith the compression of the air in the radial air bearings.

In order to prevent this, the radial air bearings may be omitted andLorentz force actuators (linear motors) used in the θZT drivingmechanism may also be used for fine movement in the X and Y directions.However, in such a case, it is extremely difficult for the Lorentz forceactuators (linear motors) to generate enough force to hold the weight ofthe top plate, the wafer and the wafer chuck mounted on the top plate aswell as to accelerate them because of restrictions on the size of themotors and heat emitted from the motors.

In addition, in the positioning apparatus of the known art such as theXY stage unit disclosed in the Japanese Unexamined Patent ApplicationPublication No. 8-229759, because the top plate 204 is formed as a solidplate, the natural frequency thereof cannot be increased. In addition,when the hollow structure 42 disclosed in the Japanese Unexamined PatentApplication Publication No. 11-142555 is used, the hollow structurecannot be formed if there is a difference in the coefficient of thermalexpansion between the ceramic bonding material and the material of thehollow structure. Accordingly, materials having small coefficients ofthermal expansion cannot be used. In addition, when an adhesive is used,differences occur between components even when they are formed in thesame shape, and the natural frequency of the combined unit cannot be ashigh as a calculated or theoretical value because of differences betweenadhesion conditions.

In addition, when a material having a small coefficient of thermalexpansion is used, since the top plate is formed as a solid plate, thethickness of the top plate is increased in order to ensure sufficientrigidity. Thus, the weight of the top plate is considerably increasedrelative to the increase in rigidity. Accordingly, the load placed onthe above-described linear motors for acceleration is increased, and acurrent necessary to hold this acceleration is also increased. Inaddition, heat emitted from the linear motors increases proportionallyto the square of the current. This degrades the environment around thewafer, and a problem occurs in that the alignment accuracy and stageaccuracy are adversely affected and productivity is reduced whenhigh-speed micromachining of semiconductor devices is required.

SUMMARY OF THE INVENTION

The present invention provides a positioning apparatus including amovable body having excellent controllability, and which can bepositioned at high speed and with high accuracy.

These advantages can be obtained according to one aspect of the presentinvention, in which a positioning apparatus which moves an objectcomprises a first plate unit that retains the object and a second plateunit that retains the first plate unit. The second unit is composed of aceramic material and comprises a hollow structure having a hollowsection, the hollow structure including a rib and holes that provide aconnection between an interior and an exterior of the hollow section.

For example, according to the present invention, a positioning apparatuswhich moves an object includes a first plate unit (wafer chuck) thatretains the object and a second plate unit (top plate unit) that retainsthe first plate unit and comprises at least one of a low thermalexpansion material having a coefficient of thermal expansion of 1.0e⁻⁶(1/° C.) or less, an inorganic fiber composite, and a SiC compositecontaining SiC and Si. The second plate unit comprises a hollowstructure having a hollow section, the hollow structure including a ribto increase the natural frequency of the second plate unit with respectto the torsional mode. In addition, the second plate unit has holes forproviding connection between the interior and exterior of the hollowsection.

In another aspect of the invention, the second plate unit includes anupper plate, a lower plate, and a plurality of side plates surroundingthe upper plate and the lower plate. The rib extends from one of theplurality of side plates at an intermediate region thereof to anintermediate region of another of the plurality of side plates.

In yet another aspect of the invention, a positioning apparatus whichmoves an object comprises a first plate unit that retains the object anda second plate unit that retains the first plate unit. The second plateunit is composed of a ceramic material and comprises a rib and aplurality of side plates on a periphery of the second plate unit. Therib extends from an intermediate region of one of the plurality of sideplates to an intermediate region of another of the plurality of sideplates, with the intermediate region of each side plate of the pluralityof side plates being separated from an end of the each side plate.

In still another aspect of the present invention, a positioningapparatus which moves an object comprises a first plate unit thatretains the object and a second plate unit that retains the first plateunit. The second plate unit is composed of a ceramic material andcomprises a hollow structure having a hollow section, with the hollowstructure including a rib and a plurality of side plates on a peripheryof the second plate unit. The rib extends from an intermediate region ofone of the plurality of side plates to an intermediate region of anotherof the plurality of side plates, the intermediate regions of each sideplate of the plurality of side plates being separated from an end ofeach side plate.

In another aspect of the invention, the second plate unit includes anupper plate and a lower plate that are formed integrally with the rib,and holes for providing a connection between the interior and exteriorof the hollow structure. In addition, the rib comprises a first rib unithaving a rectangular shape in cross section and a second rib unit havinga diamond shape in cross section. The first and second rib units arealternately disposed inside each other and bonded to each other.

When the positioning apparatus serves as a substrate-moving stage in asemiconductor exposure apparatus, the object may be either aphotosensitive substrate or an original plate having an exposurepattern. Preferably, the wafer chuck, the top plate unit, and opticalmirrors used for determining a relative position of the object such as awafer are all composed of the same material having a hollow structure.

The top plate unit may have a short-stroke electromagnetic actuator unitthat moves the object with six degrees of freedom to a predeterminedposition and a mechanism for supporting the top plate unit againstgravity.

Preferably, the positioning apparatus according to the present inventionfurther includes a long-stroke electromagnetic actuator unit that movesthe top plate unit in X and Y directions in long strokes and an X stagethat is moved by the long-stroke electromagnetic actuator unit andsupports both of the short-stroke electromagnetic actuator unit and themechanism for supporting the top plate unit against gravity.

Preferably, the short-stroke electromagnetic actuator unit includes atleast three Lorentz force actuators for moving the object in thehorizontal direction and the yaw direction to the predeterminedposition. In addition, preferably, the short-stroke electromagneticactuator unit further includes electromagnetic actuators which modulatean acceleration for moving the object in the horizontal direction. Inorder to reduce the distance between the center of gravity of the topplate unit and a power point of the Lorentz force actuators and theelectromagnetic actuators, the top plate unit to which theelectromagnetic actuators are attached preferably includes a hollowstructure having an open area at the bottom side thereof. In addition,coils and magnets of the Lorentz force actuators are arranged such thata thrust constant is within several percent of a maximum thrust constantwhen the object is at a position where an exposure process is performed.

In addition, preferably, the positioning apparatus further includes atleast three Lorentz force actuators for controlling the position of theobject in a vertical direction, a pitch-direction, and a roll-direction,the Lorentz force actuators having sufficient strokes for moving the topplate unit, which conveys the object. Furthermore, preferably, thepositioning apparatus further includes a weight-compensation mechanism,which includes magnets for generating a repulsive force or an attractiveforce, a coil spring, etc., and generates a force corresponding to atotal weight of the top plate unit, the wafer and the wafer chuckattached to the top plate unit, and perhaps movable members of theLorentz force actuators, electromagnetic actuators, and theweight-compensation mechanism, in order to support the total weightagainst gravity.

In order to prevent deformation of the top plate unit, the mirrors, thewafer, etc., due to heat emitted from the actuators, coils of theactuators may be attached to the X stage. A pipe or a wire for feedingelectricity, gas, or liquid from the upper plate of the X stage to thewafer chuck, etc., mounted on the top plate unit may be disposed ateither a central area or a peripheral area of the top plate unit. Insuch a case, the vibration transmissibility due to the pipe or the wireis reduced.

Preferably, the upper plate of the X stage has at least three supportingrods that temporarily support the object when the object is moved from aconveyor hand to the wafer chuck. The supporting rods extend through thewafer chuck and the top plate unit or second plate unit, and when thetop plate unit is moved in the vertical direction by the Lorentz forceactuators and the weight-compensation mechanism, the supporting rodsproject from the top surface of the wafer and temporarily support theobject.

In addition, in a finishing process of a surface of the second plateunit, particles may be injected into the hollow section of the hollowstructure through the holes for providing connection between theinterior and exterior of the hollow section. When the weight of thehollow section filled with the particles is made the same as the weightobtained if the hollow section is filled with the same material as thematerial of the second plate unit, a constant surface pressure isapplied during a lapping process, so that the surface can be processedwith high accuracy. In addition, a process of forming the mirrorsurfaces for determining the relative position of the object may beperformed after mechanically fixing a third plate unit to the secondplate unit.

As described above, according to the present invention, the top plateunit, which serves as a movable body in the positioning apparatus, iscomposed of at least one of a low thermal expansion material having acoefficient of thermal expansion of 1.0e⁻⁶ (1/° C.) or less, aninorganic fiber composite, and a SiC composite containing SiC and Si, inan integral, hollow structure. Accordingly, a light, strong, rigid topplate unit that is not easily deformed by heat is obtained. In addition,due to the electromagnetic couplings and the Lorentz force actuators ofthe top plate unit, a positioning apparatus having a highcontrollability is obtained. Furthermore, when a lapping process isperformed after the particles are injected into the hollow section, aconstant surface pressure is applied, so that the surface can beprocessed with high accuracy.

Further features and advantages of the present invention will becomeapparent from the following description of the preferred embodimentswith reference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a positioning apparatus according to a firstembodiment of the present invention.

FIG. 2 is a sectional view of FIG. 1 cut along line II-II.

FIG. 3 is a sectional view of FIG. 1 cut along line III-III.

FIG. 4 is a sectional view of the positioning apparatus according to thefirst embodiment cut along a center line, showing a manner in which thepositioning apparatus operates.

FIG. 5A is a sectional view showing an example of a rib structure of ahollow plate unit included in the positioning apparatus according to thepresent invention, and FIG. 5B is a sectional view showing amodification of the rib structure shown in FIG. 5A.

FIG. 6 is a sectional view showing another example of the rib structureof the hollow plate unit included in the positioning apparatus accordingto the present invention.

FIG. 7 is a sectional view of a positioning apparatus according to asecond embodiment of the present invention cut along the center line.

FIG. 8 is a sectional view of a positioning apparatus according to athird embodiment of the present invention cut along the center line.

FIG. 9 is a diagram showing a manner in which the hollow plate unitaccording to the embodiments of the present invention is processed.

FIG. 10 is a diagram showing a manner in which a mirror surface of thehollow plate unit according to the present invention is subjected to alapping process.

FIG. 11 is a diagram showing a manner in which a chuck-attaching surfaceof the hollow plate unit according to the present invention is subjectedto a finishing process.

FIG. 12 is a perspective view of a known positioning apparatus.

FIG. 13 is a control block diagram for each degree of freedom of theknown positioning apparatus.

FIG. 14 is a diagram showing gain/phase characteristics of the controlsystem of the known positioning apparatus.

FIG. 15 is a perspective view showing a hollow structure of a knownstage component.

FIG. 16 is a sectional view of a θZT driving mechanism mounted on aknown stage device.

FIG. 17 is a perspective view of a long-stroke X stage.

FIG. 18 is a diagram showing five patterns (no ribs, diamond-shaped,cross-shaped, circular, and X-shaped) of the rib structure of the hollowplate unit.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Positioning apparatuses according to embodiments of the presentinvention will be described in detail below with reference to theaccompanying drawings, considering a case in which a moved object is awafer which serves as a photosensitive substrate as an example. Thepresent invention may also be applied in a case in which the movedobject is an original plate having an exposure pattern.

First Embodiment

FIG. 1 is a schematic top view of a top plate included in a positioningapparatus according to a first embodiment of the present invention andperipheral regions thereof. FIG. 2 is a sectional view of FIG. 1 cutalong line II-II and FIG. 3 is a sectional view of FIG. 1 cut along lineIII-III. The positioning apparatus includes a wafer chuck 1 which servesas a first plate unit, a hollow plate unit 2 which serves as a secondplate unit and retains the chuck 1, a mirror 3, electromagneticcouplings 4, weight-compensation mechanisms 6, supporting rods 8, andX-direction fine-movement linear motors LMX, Y-direction fine-movementlinear motors LMY, and Z-direction fine-movement linear motors LMZ usedfor finely adjusting the position of the hollow plate unit 2, etc. Theabove-described components are disposed on an upper plate 51 a of an Xstage.

The hollow plate unit 2 shown in the figures is constructed by firstforming an integral, hollow structure, and then sintering it. The hollowplate unit 2 may be formed by using inorganic fiber composites or SiCcomposites containing SiC and Si, and the entire body thereof is formedof a single material by the sintering process. Since the hollowstructure is formed without bonding two or more dissimilar materials andwithout using an adhesive or glass bonding in the resintering process,reduction in rigidity at the bonded portions does not occur as in theknown art.

In the case in which a low thermal expansion material having a smallcoefficient of thermal expansion such as 1.0e⁻⁶ (1/° C.) or less or SiCis used, the co-sintering process for obtaining the hollow structurecannot be performed. Accordingly, two or more members must be bondedtogether. Also in this case, when the members are bonded together bymetal bonding instead of using an adhesive or glass bonding, thedifference in the coefficient of linear expansion can be compensatedfor, so that reduction in rigidity at bonded portions does not occur asin the known art. Thus, an integral, hollow structure formed of a singlematerial is obtained.

In addition, in order to ensure the rigidity, the hollow plate unit 2has a rib structure similar to those shown in FIGS. 5A, 5B, and 6, andthrough holes H2 a, shown in FIG. 2, are formed for allowing ambient gasto pass therethrough and providing connection between the interior andexterior of a hollow section H2 having the rib structure. The externalenvironment may be, for example, the atmosphere, a N₂ environment, a Heenvironment, a vacuum environment, etc. Although the hollow structure ismanufactured in an inactive-gas environment, this environment isdifferent from those in which the hollow plate unit 2 is mounted on thestage or in which the positioning apparatus is stored. The through holesH2 a are formed in order to avoid a situation that the residual gascaptured inside the hollow plate unit 2 leaks into the externalenvironment and degrades the environment around the stage, which makesit difficult to increase the degree of vacuum.

The wafer chuck 1 for receiving a wafer W, which is a photosensitivesubstrate, is disposed on the top surface of the hollow plate unit 2.The chuck 1 is fixed to the hollow plate unit 2 by air suction or amechanical clamp (not shown), and the wafer W is retained on the chuck 1by air suction or an electrostatic force (not shown).

In addition, the mirror 3 is provided for determining the relativeposition of the wafer W. Although only one mirror 3 is shown in FIG. 2,a plurality of mirrors are provided in actuality in order to determinethe position in six degrees of freedom. Although the top surface of themirror 3 should be viewed from the top, it is omitted in FIG. 1. Themirror 3 is fixed to the hollow plate unit 2 by, for example, a methoddisclosed in Japanese Unexamined Patent Application Publication No.5-19157.

The chuck 1 and the mirror 3 are formed of the same material as thehollow plate unit 2, so that they have the same coefficient of thermalexpansion and the same coefficient of thermal conductivity. Accordingly,even when the temperature of the hollow plate unit 2 varies due to heatcaused in an exposure process or heat emitted from actuators,deformation due to the difference in coefficient of thermal expansiondoes not occur between the hollow plate unit 2 and the mirror 3 orbetween the hollow plate unit 2 and the chuck 1. In addition, the chuck1 and the mirror 3 have hollow structures and include hollow sections H1and H3, respectively, so that the weights thereof are reduced and therigidities thereof are increased. When the weights of the chuck 1 andthe mirror 3 are reduced, the natural frequency of the entire movablebody including the hollow plate unit 2 increases.

Actuators using an electromagnetic force for moving the wafer W to apredetermined position with six degrees of freedom are disposed underthe hollow plate unit 2. More specifically, two types of actuators usingthe electromagnetic force are provided: the electromagnetic couplings 4for the acceleration in the X and Y directions and fine-movement linearmotors LM which serve as Lorentz force actuators used for the positioncontrol in six degrees of freedom. The above-described actuators haveshort strokes, and are mounted on the upper plate 51 a of an X stage 51shown in FIG. 17, which has a long stroke.

Next, a Y stage 54 and the X stage 51, which serve as a long-strokestage unit, will be described below with reference to FIG. 17. The Ystage 54 is levitated above a base 55 by supplying air to hydrostaticair bearings (not shown) disposed under Y-stage guides 54 a. When air issupplied to hydrostatic air bearings (not shown) at a fixed guide 52placed at one side of the base 55 and at one of the Y stage guides 54 a,the Y stage 54 is moved in the Y direction by two drive actuators 54 cdisposed at both sides of the Y stage 54 while being guided in thehorizontal direction along the fixed guide 52. In addition, similarly tothe Y stage 54, the X stage 51 is also levitated above the base 55 bysupplying air to hydrostatic air bearings (not shown) disposed under anX stage base 51 c. When air is supplied to hydrostatic air bearings (notshown) at a side surface 54 b of the Y stage 54 and at an X stage guide51 b, the X stage 51 is moved in the X direction by drive actuators 51 dwhile being guided in the horizontal direction along the side surface 54b. The X stage 51 and the Y stage 54 are maintained at a predeterminedorientation by a plurality of pressurizing magnet units. Laserinterferometers (not shown) are provided on the long-stroke stage unit.Optical mirrors similar to those disposed on the top plate of the knownart may be disposed on the top surface of the X stage 51 for the laserinterferometers. Alternatively, an optical mirror may be provided oneach of flat portions 54 d of the Y stage 54 for the Y direction, andthe position of the X stage 51 may be determined by determining theposition of the optical mirror disposed on the X stage 51 relative tothe Y stage 54. This long-stroke stage unit may have the sameconstruction as the stage device disclosed in the Japanese UnexaminedPatent Application Publication No. 8-229759 except for the laserinterferometers used for controlling the long-stroke stage unit.

According to a known technique, in final position control in the X and Ydirections, the wafer W is moved by the drive actuators 54 c and 51 dhaving long strokes via the radial air bearings. In the presentembodiment, the final position control in the X and Y directions isperformed by using the above-described fine-movement linear motors LMXand LMY, which are Lorentz force actuators disposed under the hollowplate unit 2. Accordingly, a long-stroke stage unit having a relativelylow control performance may also be used, so that the component cost andadjustment cost can be reduced. In addition, it is not necessary to usethe Lorentz force actuators as the long-stroke actuators, and othertypes of linear motors in which more importance is placed on heatemission or thrust may also be used.

The electromagnetic couplings 4 transmit an acceleration generated bythe long-stroke actuators to the fine-movement unit including the hollowplate unit 2. Since a single electromagnetic coupling generates only anattractive force, two electromagnetic couplings 4 are disposed such thatthey oppose each other in the X direction, as shown in FIG. 2. Inaddition, although not shown in the figure, two electromagneticcouplings 4 are disposed such that they oppose each other in the Ydirection, that is, in the direction perpendicular to the page in FIG.2. Each of the electromagnetic couplings 4 includes a fixed member 4 battached to the upper plate 51 a of the X stage at the central regionthereof and a movable member 4 a attached to the hollow plate unit 2.From the viewpoint of heat emission and the mounting process, coils (notshown) of the electromagnetic couplings 4 are disposed on the fixedmembers 4 b. The movable members 4 a and the fixed members 4 b are bothformed by using electromagnetic steel plates, and laminated steel platesof the fixed members 4 b have an E shape or a U shape so that the coilscan be wound around it. In each of the electromagnetic couplings 4, asufficient gap is formed between the movable member 4 a and the fixedmember 4 b. The amount of this gap is determined on the basis of thesurface-processing accuracy and the fabrication accuracy of theelectromagnetic couplings 4, a stroke required for the movement in sixdegrees of freedom for position control or wafer alignment, and thedifference between the position of the X stage 51 controlled by thelong-stroke actuators and the position of the fine-movement unit duringacceleration (control residual of the long-stroke unit). In addition,the opposing surfaces of the electromagnetic couplings 4 are formedalong cylindrical surfaces so that they do not interfere with each otherwhen the fine-movement unit moves the wafer W in the rotationaldirection around the Z axis.

In the unit including the above-described four electromagnetic couplings4, all of the arc surfaces facing each other have the same center. Inaddition, from the viewpoint of processing accuracy, the radii thereofare preferably the same. Furthermore, the central point of the arcsurfaces in the XY plane is preferably at the same position as thecenter of gravity G of the fine-movement unit including the hollow plateunit 2.

As described above, the fine-movement linear motors LM, which are theLorentz force actuators, are disposed under the hollow plate unit 2 forthe position control in six degrees of freedom. The fine-movement linearmotors LMX and LMY used for fine movement in the X and Y directions aredisposed at the periphery of the electromagnetic couplings 4. TwoY-direction fine-movement linear motors LMY are disposed along the Xaxis, and two X-direction fine-movement linear motors LMX are disposedalong the Y direction. Yaw-direction control is performed by usingeither one of the Y-direction fine-movement linear motors LMY and theX-direction fine-movement linear motors LMX. As another arrangement ofthe fine-movement linear motors LM, either one of the X-directionfine-movement linear motors LMX and the Y-direction fine-movement linearmotors LMY may be reduced to one and be disposed at the center ofgravity of the fine-movement unit. In the X-direction and Y-directionfine-movement linear motors LMX and LMY, magnets and yokes are disposedon the movable members LMX1 and LMY1, and coils which emit heat aredisposed on the fixed members LMX2 and LMY2 from the viewpoint of heatemission and the mounting process.

In order to control the movement in the Z direction, pitch direction,and roll direction, three Z-direction fine-movement linear motors LMZare placed under the hollow plate unit 2, as shown in FIG. 1. FIG. 3 isa sectional view of FIG. 1 cut along line III-III. Similar to theX-direction and Y-direction fine-movement linear motors LMX and LMY, theZ-direction fine-movement linear motors LMZ, magnets and yokes aredisposed on the movable members LMZ1 and coils which emit heat aredisposed on the fixed members LMZ2 from the view of heat emission andthe mounting process.

In addition, the weight-compensation mechanisms 6 are disposed under thehollow plate unit 2. As shown in FIG. 3, the weight-compensationmechanisms 6 are constructed such that the total force generated by theweight-compensation mechanisms 6 is approximately the same as the weightof the fine-movement unit. Although a residual force remains since thetotal force generated by the weight-compensation mechanisms 6 varies inaccordance with the vertical position of the hollow plate unit 2, it iscompletely eliminated by the Z-direction fine-movement linear motorsLMZ. The Z-direction fine-movement linear motors LMZ must continuouslygenerate a large thrust because of this residual force, and the totalforce generated by the weight-compensation mechanisms 6 is adjusted suchthat the environment around the hollow plate unit 2 is not degraded dueto heat emitted from the fine-movement linear motors LM. In order toreduce the variation in the generated force, each of theweight-compensation mechanisms 6 use both a pair of attracting magnets 6a and a compression spring 6 b. Alternatively, a bellowphragm or a pairof repelling magnets which produces a similar effect may also be used.

When the weight-compensation mechanisms 6 are disposed coaxially withthe Z-direction fine-movement linear motors LMZ, the hollow plate unit 2does not receive the residual force of the weight-compensation mechanism6 which cannot be removed. Accordingly, they are preferably disposedcoaxially with the Z-direction fine-movement linear motors LMZ.

Three supporting rods 8 used for temporarily supporting the wafer W whenit is exchanged are provided at the same side as the fixed members 4 bof the electromagnetic couplings 4. While the wafer W is being retainedon the chuck 1 and subjected to the exposure process, the top surfacesof the supporting rods 8 are positioned below the bottom surface of thewafer W. The supporting rods 8 themselves do not have a function to movevertically, and when the entire body of the hollow plate unit 2 is moveddownward by the Z-direction fine-movement linear motor LMZ, thesupporting rods 8 project from the top surface of the chuck 1, as shownin FIG. 4. Accordingly, the supporting rods 8 retain the wafer W at thebottom surface thereof. The entire body of the hollow plate unit 2 ismoved downward until the gap between the bottom surface of the wafer Wand the top surface of the chuck 1 is sufficiently increased such that aconveyor hand 9 used for conveying the wafer W can be inserted therein.Accordingly, the wafer W can be exchanged by using the conveyor hand 9.

The position of the mirror 3 in the vertical direction is determinedsuch that the measurement using the laser interferometer can beperformed even when the hollow plate unit 2 is moved downward from aposition where the exposure process is performed (hereinafter referredto as a exposure position) in order to exchange the wafer W, etc.

As shown in FIG. 4, the magnets and the coils of the X-direction,Y-direction, and Z-direction fine-movement linear motors LMX, LMY, andLMZ are arranged such that the thrust can be generated even when thehollow plate unit 2 is at a position higher than the exposure positionfor cleaning the chuck 1 or at a position lower than the exposureposition for exchanging the wafer W. Since the wafer W is exchanged in ashort time and only a small amount of heat is emitted, it is notnecessary to generate a thrust as high as that generated when the hollowplate unit 2 is at the exposure position. Thus, the size of thefine-movement linear motors LM is preferably reduced by reducing thethrust constant by approximately 10% compared to when the hollow plateunit 2 is at the exposure position. When large fine-movement linearmotors LM are used to obtain the same thrust at every position, the sizeof the magnets is increased and the weight of the fine-movement unit isincreased accordingly. Accordingly, load placed on the electromagneticcouplings 4 during acceleration increases and heat is emitted from theelectromagnetic couplings 4, which degrades the surrounding environment.In addition, a problem occurs in that the temperature of the hollowplate unit 2 increases due to the heat generated and the distancebetween the wafer W and the mirror 3 varies. In addition, load placed onthe large-stroke linear motors also increases. Furthermore, when theheight of the fine-movement linear motors LM in the Z directionincreases along with the increase in size thereof, the distance betweenthe center of gravity G of the fine-movement unit and the driving point(power point) of the long-stroke linear motors also increases.Accordingly, a moment is applied to the X stage 51, and load placed onthe hydrostatic air bearings disposed under the bottom surface of the Xstage 51 increases. Since the load placed on the hydrostatic airbearings per unit of area preferably is maintained constant, the area ofthe bottom surface of the X stage 51 increases. When the size of the Xstage 51 increases, the X linear motors used for transferring the Xstage 51 and the Y linear motors used for transferring the X linearmotors receive larger loads. In this manner, loads are successivelyincreased from the wafer side toward the base side. Therefore, in thepresent embodiment, it is important to reduce the size of thefine-movement linear motors LM. As shown in FIG. 2, the fine-movementlinear motors LM are constructed such that the coils and the magnets arepositioned asymmetrically (the centers thereof are not at the sameposition) at the exposure position, and the thrust constant is withinseveral percent of the maximum thrust constant at the exposure position.

The reason why the thrust constant is set to within several percent ofthe maximum thrust constant and not to the maximum thrust constant isbecause if the reduction in thrust constant caused when the hollow plateunit 2 is moved downward for exchanging wafers exceeds 20%, theinfluence of heat cannot be ignored even though the exchanging processtakes only a short time.

As shown in FIG. 2, in order to make the center of gravity of thefine-movement unit close to the power point of the electromagneticcouplings 4, the hollow plate unit 2 of the present embodiment includesan open area at the central region thereof. When the distance α is 10mm, the weight of the hollow plate unit 2 is 10 kg, and the support spanof the Z-direction fine-movement linear motors LMZ is 100 m, and thewafer W is moved at the acceleration of, for example, 1G, theZ-direction fine-movement linear motors LMZ must hold the force of 1 kgfdue to the moment determined on the basis of the distance α. In order toreduce heat emitted from the Z-direction fine-movement linear motorsLMZ, the distance α between the center of gravity G of the fine-movementunit and the power point of the electromagnetic couplings 4 ispreferably zero. On the contrary, when the electromagnetic couplings 4are disposed on the same plane as the X-direction, Y direction, andZ-direction fine-movement linear motors LMX, LMY and LMZ, the force heldby the Z-direction fine-movement linear motors LMZ increasesproportionally to the distance α, so that the size of the Z-directionfine-movement linear motors LMZ must be increased. Accordingly, themoving weight also increases, and it becomes difficult for the stageunit to function. In FIG. 2, the distance α is exaggerated in order tofacilitate understanding.

Next, construction of the hollow plate unit 2 will be described below.The hollow plate unit 2 has a rib structure to increase strength andrigidity. In addition, the hollow plate unit 2 has through holes H2 afor making the interior environment of the hollow cells formed by theribs and the external environment the same.

In the control system of the positioning apparatus according to thepresent embodiment, in order to obtain high-speed, high-accuracytracking performance, the gain characteristics of the positioningapparatus are preferably made as high as possible. For this reason, itis necessary to increase the natural frequency, which is one of themechanical characteristics of the stage unit that have been limiting thegain characteristics in known techniques. In the hollow plate unit 2according to the present embodiment, the natural frequency isconsiderably increased compared to that obtained by known techniques dueto the rib structure and the hollow section, and the gaincharacteristics of the control system are improved. Recently, inscanning exposure apparatuses, for example, it has been required toincrease the zero-crossing frequency of the stage unit itself in orderto obtain a high degree of synchronization between the wafer and thereticle, such as within several nanometers. Accordingly, thezero-crossing frequency of the hollow plate unit 2 necessary to satisfythis requirement has been increased several times. By applying thepresent invention, the hollow plate unit 2 having a high naturalfrequency can be obtained.

Next, the rib structure will be explained. FIGS. 5A and 5B are sectionalviews showing examples of the rib structure of the hollow plate unit 2.In the case in which an open area is not formed at the central region,the hollow plate unit 2 may have the rib structures shown in FIG. 5A and5B.

Rib structures having five patterns shown in FIG. 18 (no ribs,diamond-shaped, cross-shaped, circular, and X-shaped) have beenevaluated by performing eigenvalue analysis. As a result, the firstvibration mode is torsional, and the natural frequency increases in theorder from the structure having high resistance to the torsional mode tothe structure having low resistance to the torsional mode. In theabove-described five patterns, the natural frequency increases in theorder of no ribs, cross-shaped, circular, x-shaped, and diamond-shaped.Accordingly, in the rib structure according to the present invention,ribs arranged in the diamond pattern are more preferable than thosearranged in the X-shaped pattern, which is commonly used when ribs areinstalled in a base.

The ribs are formed integrally with an upper plate and a lower plate ofthe hollow plate unit 2, and side plates are disposed around the upperplate and the lower plate. Each rib extends from one of the side platesat an intermediate region, which is separated from the corners where theside plate is connected to the adjacent side plates, to an intermediateregion of an adjacent side plate.

FIGS. 5A and 5B show specific examples of the rib structure. In the ribstructure shown in FIG. 5A, a rib unit R1 having a rectangular shape incross section, the sides thereof extending along the X and Y finemovement directions, and a rib unit R2 having a diamond shape in crosssection, the sides thereof extending at an angle of 45 degrees relativeto the X and Y fine movement directions, are alternately arranged. Morespecifically, a rib unit R2 a is disposed inside a rib unit R1 a, a ribunit R1 b is disposed inside the rib unit R2 a, and a rib unit R2 b isdisposed inside the rib unit R1 b. Due to this construction, aconsiderably high natural frequency is obtained.

The present embodiment is characterized in that the electromagneticcouplings 4 are disposed at the central region. A rib structurecorresponding to this construction is shown in FIG. 6. In this ribstructure, the inner circle forming an attachment hole H2 c used forattaching the movable members 4 a of the electromagnetic couplings 4 issufficiently large so that the inner surface of the attachment hole H2 cdoes not interfere with the exterior surface of a fixed unit on whichthe fixed members 4 b of the electromagnetic couplings 4 are attached.The rib structure includes a rib unit R3 whose inner periphery has acircular shape and whose outer periphery has the shape of thecombination of a diamond and a circle. The outer region of this rib unitR3 is formed similarly to FIG. 5A, where a rectangular rib unit and adiamond-shaped rib unit are alternately disposed. More specifically, adiamond-shaped rib unit R2 a is disposed inside a rectangular rib unitR1 a, and a rectangular rib unit R1 b is disposed inside thediamond-shaped rib unit R2 a.

FIG. 5B shows a modification of FIG. 5A. In FIG. 5A, the weight at thetriangular portions at the four corners is reduced in order to increasethe neutral frequency. However, in actuality, the weight of the mirror3, etc., is placed thereon. In such a case, the neutral frequency can beeffectively increased by forming ribs which extend from intermediateregions Rw of the side plates, at which resistance to torsion is small,rather than forming ribs which extend diagonally from the corners atwhich the side plates are connected to each other.

In the present embodiment, the thickness of the ribs is preferably setto approximately 5 mm according to calculations. Even when the thicknessis increased to 10 mm, the natural frequency increases only by a smallamount. In the case in which a SiC composite containing SiC and Si isused, the process of sintering each member of the hollow structure inadvance is not performed. Accordingly, it is not necessary to increasethe thickness of the ribs in order to obtain sufficient bonding areas orto maintain the strength of each member in the sintering process. In thepresent embodiment, the rib structure of the hollow plate unit 2 isformed before the final sintering process. Thus, there is an advantagein that the strength of the hollow plate unit before the sinteringprocess is also ensured. Since it is not necessary to increase thethickness of the ribs which provide the bonding surfaces even though thenatural frequency cannot be increased, as in the known art, the weightof the hollow plate unit 2 can be prevented from being increased morethan necessary. Accordingly, the weight of the hollow plate unit 2 isreduced, and the load placed on the linear motors for acceleration isalso reduced. In addition, the current required for generating asufficient force to hold this acceleration is also reduced and heatemitted from the linear motors is considerably reduced. Accordingly, theadverse influence on the environment is reduced and the positioningaccuracy is increased.

When an inorganic fiber composite is used, since the specific rigiditythereof is high, the weight is further reduced and the rigidity isfurther increased.

In addition, according to the known art, the top plate cannot be formedof a low thermal expansion material having a small coefficient ofthermal expansion such as 1.0e⁻⁶ (1/° C.) or less if the low thermalexpansion material is a cordierite-based material, since the Young'smodulus thereof is low. However, according to the present invention, thehollow plate unit having the rib structure may also be formed of lowthermal expansion materials.

In addition, similar effects can of course be obtained also when SiChaving a high Young's modulus is used in order to obtain a higherrigidity than when SiC composites are used.

Second Embodiment

FIG. 7 is a schematic sectional view of a positioning apparatusaccording to a second embodiment of the present invention which includesa mirror-combined hollow plate unit constructed by adhering ormechanically fixing an optical mirror 3 on a hollow plate unit 2 at aside surface thereof.

In order to avoid deformation of the hollow plate unit 2 due to thedifference in coefficient of thermal expansion, the optical mirror 3 andthe hollow plate unit 2 are formed of the same material. Since they areintegrally formed using the same material, the displacement of themirror 3 due to the acceleration of the stage movement can be prevented.In addition, since the mirror 3 is retained by the hollow plate unit 2having a high rigidity, deformation of the mirror 3 can also beprevented.

Pipes, wires, etc., used for transferring electricity, gas, and liquidto the chuck 1 and sensors (not shown) mounted on the hollow plate unit2 from the upper plate 51 a of the X stage 51 are disposed at thecentral area or the most peripheral area of the hollow plate unit 2, sothat the vibration transmissibility due to the pipes and the wires arereduced. In order to reduce the vibration transmissibility, as shown inFIG. 7, a relatively hard pipe which receives internal pressure fromair, etc., is constructed such that the air flows through an inductionpipe 11 formed at the central area of the fixed members of theelectromagnetic couplings 4, a connecting tube 13 which providesvertical connection, an induction pipe 15 formed at the central area ofthe movable members of the electromagnetic couplings 4, and the centralarea of the hollow plate unit 2, and is supplied to a chucking vacuumgroove 18 formed in the chuck 1.

In the above-described construction, an element which determines thevibration transmissibility is the connecting tube 13. Since theconnecting tube 13 is disposed at the central area, asymmetricinterference does not easily occur and the controllability can beprevented from being degraded. In addition to disposing the connectingtube 13 at the central area, the length thereof is preferably increasedand it is preferably formed in a helical shape in order to reduce theinfluence of the connecting tube 13. Cables having a relatively highflexibility such as an electric cable 17 are preferably disposed at theperiphery of the hollow plate unit 2 since the influence on vibration issmall. Signal cables are preferably disposed at the periphery ratherthan being disposed at the center similarly to the air pipe tube, sothat broken wires can be easily exchanged.

Next, a method for processing the hollow plate unit 2 will be described.When a finishing process of the optical mirror surface is performed,first, the mirror 3 is fixed to the hollow plate unit 2 as describedabove. Then, as shown in FIG. 9, particles (spherical or cylindrical) 20are injected into the hollow section of the hollow structure through thethrough holes H2 a formed in the hollow plate unit 2 for allowing theambient gas to pass therethrough. By injecting the particles 20, theweight of the hollow section filled with the particles 20 is made thesame as the weight obtained if the hollow section is filled with thesame material as the material of the hollow structure. In the case inwhich the particles 20 have a cylindrical shape and are arranged orderlyand the specific gravity of the SiC composite is 3.0, the specificgravity of the particles 20 are determined as 3.8. Accordingly,particles formed of alumina ceramics can be used.

When the particles 20 are injected, the surface pressure applied duringgrinding, lapping, and polishing processes is made the same as thesurface pressure applied when a solid plate is used. In particular, whena high-precision flat surface is formed by using a lapping plate 22, theamount of processing varies in accordance with the surface pressure.However, this can be compensated for by filling the hollow section withthe particles 20. FIG. 10 is a diagram showing a manner in which thesurface of the mirror 3 is subjected to a lapping process. FIG. 11 is adiagram showing a manner in which the surface 2 a of the hollow plateunit 2, which receives the chuck, is subjected to a finishing process.This method is not limited to the case in which the surface of themirror 3 of the hollow plate unit 2 is processed, and may also beapplied to other hollow components whose surface must have the flatnessof 1 μm or less such as hollow guides, etc.

Third Embodiment

FIG. 8 is a diagram showing a positioning apparatus according to a thirdembodiment of the present invention. In FIG. 2, the hollow plate unit 2includes a solid-plate area at a region where the movable members 4 a ofthe electromagnetic couplings 4 are attached. However, in such a case,the hollow plate unit 2 will be deformed if the acceleration applied tothe electromagnetic couplings 4 is large. When the hollow plate unit 2is deformed, the chuck 1 is also deformed, and as a result, the wafer Wis also deformed so that an alignment error occurs. Therefore, accordingto the third embodiment of the present invention, in order to increasethe strength of the hollow plate unit 2, the region of the hollow plateunit 2 where the movable members 4 a of the electromagnetic couplings 4are attached is also formed in a hollow structure instead of merelyincreasing the thickness thereof, so that the weight is reduced and therigidity is increased.

While the present invention has been described with reference to whatare presently considered to be the preferred embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments. On the contrary, the invention is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims. The scope of the following claims is to beaccorded the broadest interpretation so as to encompass all suchmodifications and equivalent structures and functions.

1. A positioning apparatus which moves an object, said apparatuscomprising: a first plate unit that retains the object; and a secondplate unit that retains said first plate unit, said second plate unitcomposed of a ceramic material and comprising a hollow structure havinga hollow section, said hollow structure including a rib and holes thatprovide a connection between an interior and an exterior of the hollowsection.
 2. A positioning apparatus according to claim 1, wherein saidsecond plate unit includes an upper plate and a lower plate that areformed integrally with said rib.
 3. A positioning apparatus according toclaim 1, wherein said second plate unit includes an upper plate, a lowerplate, and a plurality of side plates surrounding said upper plate andsaid lower plate, and said rib extends from one of said plurality ofside plates at an intermediate region thereof to an intermediate regionof another of said plurality of side plates.
 4. A positioning apparatusaccording to claim 1, wherein said rib comprises a first rib unit havinga diamond cross section, a second rib unit disposed within said firstrib unit having a rectangular cross section, and a third rib unitdisposed within said second rib unit having a circular cross section. 5.A positioning apparatus according to claim 1, wherein said rib comprisesa first rib unit having a rectangular shape in cross section and asecond rib unit having a diamond shape in cross section, said first andsecond rib units being alternately disposed inside each other and bondedto each other.
 6. A positioning apparatus according to claim 5, whereinsaid second plate unit comprises at least one of a low thermal expansionmaterial having a coefficient of thermal expansion of 1.0e⁻⁶ (1/° C.) orless, an inorganic fiber composite, and a SiC composite containing SiCand Si.
 7. A positioning apparatus according to claim 6, wherein saidpositioning apparatus serves as a substrate-moving stage in asemiconductor exposure apparatus, and wherein the object is either aphotosensitive substrate or an original plate having an exposurepattern. 8-22. (Cancelled)
 23. A positioning apparatus according toclaim 1, wherein said first plate unit and said second plate unit areformed of a same material and said first plate unit includes a hollowstructure.
 24. A positioning apparatus according to claim 1, whereinsaid second plate unit includes a third plate unit that determines arelative position of the object and includes a plurality of opticalmirrors, said third plate unit composed of a same material as saidsecond plate unit, said positioning apparatus further comprising a firstactuator unit that moves the object with six degrees of freedom to apredetermined position by an electromagnetic force and a mechanism forsupporting said second plate unit against gravity.
 25. A positioningapparatus according to claim 24, further comprising: a second actuatorunit that moves said first plate unit in X and Y directions in longstrokes; and a fourth plate unit that is moved by said second actuatorunit and supports said first actuator unit and said mechanism forsupporting said second plate unit against gravity.
 26. A positioningapparatus according to claim 24, wherein said first actuator unitincludes at least three Lorentz force actuators for moving the object inthe horizontal direction and the yaw direction to the predeterminedposition and at least four electromagnetic actuators which are disposedconcentrically and which modulate an acceleration for moving the object,each one of said at least four electromagnetic actuators including amovable member affixed to said hollow structure of said second plateunit, the hollow section of said hollow structure being an open area ata central region of said hollow structure, the open area serving toreduce the distance between the center of gravity of said second plateunit and a power point of each of said Lorentz force actuators and saidelectromagnetic actuators.
 27. A positioning apparatus according toclaim 26, wherein said Lorentz force actuators include coils and magnetsthat are arranged such that a thrust constant is within several percentof a maximum thrust constant when the object is at a position where anexposure process is performed.
 28. A positioning apparatus according toclaim 25, wherein said fourth plate unit includes at least threesupporting rods for temporarily retaining the object when the object ismoved from a conveyor hand to said first plate unit, said supportingrods extending through said first plate unit and said second plate unitand projecting from a top surface of said first plate unit in accordancewith a vertical movement of said second plate unit by said firstactuator unit.
 29. A positioning apparatus according to claim 25,further comprising at least one of a pipe and a wire for transferring atleast one of electricity, gas, and liquid supplied from said fourthplate unit to said second plate unit, said at least one of the pipe andthe wire being disposed at either a central area or a peripheral area ofsaid second plate unit.
 30. A positioning apparatus according to claim1, further comprising at least three Lorentz force actuators forcontrolling the object in a vertical direction, a pitch-direction, and aroll-direction.
 31. A positioning apparatus according to claim 1,further comprising a weight-compensation mechanism that generates aforce corresponding to a total weight of said second plate unit andcomponents mechanically fixed to said second plate unit in order tosupport the total weight against gravity.
 32. A method for manufacturinga positioning apparatus according to claim 1, in which the hollowstructure requires a finished surface having a flatness of 1 mm or less,said method comprising the steps of: injecting particles into the hollowsection of the hollow structure through holes formed in the hollowstructure; and performing manufacturing processes such that a weight ofthe hollow section filled with the particles is the same as the weightobtained if the hollow section is filled with the same material as thematerial for the second plate unit.
 33. A method for manufacturing apositioning apparatus according to claim 24, comprising the steps of:mechanically affixing the third plate unit to the second plate unit; andthen forming mirror surfaces for determining a relative position of theobject.
 34. A positioning apparatus which moves an object, saidapparatus comprising: a base plate unit; a first plate unit that ismovable with respect to said base plate and retains the object; and asecond plate unit that retains said first plate unit, said second plateunit being composed of a ceramic material and comprising a hollowstructure having a hollow section, said hollow structure including a riband holes that provide a connection between an interior and an exteriorof the hollow section.
 35. A positioning apparatus according to claim34, further comprising an actuator between said second plate unit andsaid base plate unit, and wherein said second plate unit has an openarea at the position of said actuator.